In this work a technique capable to investigate the near-wake stability properties of a wind turbine immersed in the atmospheric boundary layer is presented. Specifically, a 2D local spatial stability analysis is developed in order to take into account typical flow features of real operating wind turbines, such as the presence of the atmospheric boundary layer and the turbulence heterogeneity of the oncoming wind. This stability analysis can be generally applied on either experimental measurements or numerical data. In this paper it was carried out on wind tunnel experiments, for which a downscaled wind turbine is immersed in a turbulent boundary layer. Through spatial stability analysis, the dominant mode in the near wake, i.e. the most amplified one, is characterized and its frequency matches the hub-vortex instability frequency measured in the wind tunnel. As in the case of [10], where an axisymmetric wake condition was investigated, the hub-vortex instability results in a single-helical mode.